Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.io.*;
import java.lang.*;

public class A192
{

public static void main(String args[])
{

BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
String s="";

try
{
s=br.readLine();
}
catch(IOException io)
{
System.out.println("error");
}

long n=Long.parseLong(s);

boolean flag=true,res=false;
long i=1,num=0;

while(flag)
{
num=(i*(i+1))/2;

if(num>=n)
{break;}
else
{
res=check(n-num);
if(res==true)
{System.out.println("YES");
break;}
}
i++;
}
if(res==false)
{
System.out.println("NO");
}
}
static boolean check(long num)
{
double t=Math.sqrt((8*num)+1);
if(Math.floor(t)==t)
{
if(t%2!=0)
{return true;}
}
return false;
}
}